Should I use regression analysis after chi-square test?

[Artem Abduramanov]

Hello!

The research question is whether the employer-provided health insurance reduces the likelihood of employee turnover (the intentions to leave the job among employees). My response variable is binary (yes/no). The variable of interest is categorical (4 categories: 0- no health insurance, 1-employer-provided health insurance, 2-own health insurance, 3-other sponsor of health insurance)

I made a chi-square test, which shows the the differences in means is not statistically significant (p>0.05).

Does it mean that I should stop and not continue dealing with regression analysis to find out the relationship between the variables (and magnitude of that relationship)? Can regression model with the list of control variables provide me with the opposite significant result?

Would be glad for answers!

Artem.

[Clyde Schechter]

It is entirely possible that a multivariable analysis will produce results very different, including opposite direction of effect, from what you find in a bivariate analysis. This is known as Simpson's paradox. The Wikipedia page about it is very good and I recommend it to you.

After familiarizing yourself with this phenomenon, you then need to think carefully about exactly what you are trying to learn from your data, and whether the bivariate model or a multivariate analysis is the correct one to answer your actual question. What you should not do is run both models and then pick the one whose results best accord with your desired conclusion.